On the quantization of the Kowalevskaya top

The equations of motion of a heavy top can be integrated for three different combinations of the parameters of the system. Historically, the discovery of these three integrable cases is attributed to Euler, Lagrange and Kowalevskaya, respectively. While the quantization of the first two cases can be performed in a straightforward way, the quantum integrability of the Kowalevskaya top is far from trivial. We show here how one can recover quantum integrability for this case as well.     

On the discrete form of the Fokas–Ablowitz equation

The Fokas–Ablowitz equation, quadratic in the second derivative, is obtained from Painlevé VI by a Miura transformation. We present here two different discretisations in terms of difference- and multiplicative, q-, equations.     

Integrability of the Hirota-Satsuma equations: Two tests

We examine the Hirota-Satsuma equation from the point of view of integrability. We show that the equation satisfies the Painlevé criterion, which according to the Ablowitz-Ramani-Segur conjecture makes it a candidate for integrability. Moreover we show that the two different kinds of solitons discovered by Hirota and Satsuma can be freely added, another indication of integrability.     

Engineering Chemically Exfoliated Large‐Area Two‐Dimensional MoS2 Nanolayers with Porphyrins for Improved Light Harvesting

Molybdenum disulfide (MoS₂) is a promising candidate for electronic and optoelectronic applications. However, its application in light harvesting has been limited in part due to crystal defects, often related to small crystallite sizes, which diminish charge separation and transfer. Here we demonstrate a surface‐engineering strategy for 2D MoS₂ to improve its photoelectrochemical properties. Chemically exfoliated large‐area MoS₂ thin films were interfaced with eight molecules from three porphyrin families: zinc(II)‐, gallium(III)‐, iron(III)‐centered, and metal‐free protoporphyrin IX (ZnPP, GaPP, FePP, H₂PP); metal‐free and zinc(II) tetra‐(N‐methyl‐4‐pyridyl)porphyrin (H₂T4, ZnT4); and metal‐free and zinc(II) tetraphenylporphyrin (H₂TPP, ZnTPP). We found that the photocurrents from MoS₂ films under visible‐light illumination are strongly dependent on the interfacial molecules and that the photocurrent enhancement is closely correlated with the highest occupied molecular orbital (HOMO) levels of the porphyrins, which suppress the recombination of electron–hole pairs in the photoexcited MoS₂ films. A maximum tenfold increase was observed for MoS₂ functionalized with ZnPP compared with pristine MoS₂ films, whereas ZnT4‐functionalized MoS₂ demonstrated small increases in photocurrent. The application of bias voltage on MoS₂ films can further promote photocurrent enhancements and control current directions. Our results suggest a facile route to render 2D MoS₂ films useful for potential high‐performance light‐harvesting applications.     

Preliminary investigations on the antibacterial activity of zinc oxide nanostructures

We have fabricated electroactive multilayer thin films containing ferritin protein cages. The multilayer thin films were prepared on a solid substrate by the alternate electrostatic adsorption of (apo)ferritin and poly(N-isopropylacrylamide-co-2-carboxyisopropylacrylamide) (NIPAAm-co-CIPAAm) in pH 3.5 acetate buffer solution. The assembly process was monitored using a quartz crystal microbalance. The (apo)ferritin/poly(NIPAAm-co-CIPAAm) multilayer thin films were then cross-linked using a water-soluble carbodiimide, 1-[3-(dimethylamino)propyl]-3-ethylcarbodiimide. The cross-linked films were stable under a variety of conditions. The surface morphology and thickness of the multilayer thin films were characterized by atomic force microscopy, and the ferritin iron cores were observed by scanning electron microscopy to confirm the assembly mechanism. Cyclic voltammetry measurements showed different electrochemical properties for the cross-linked ferritin and apoferritin multilayer thin films, and the effect of stability of the multilayer film on its electrochemical properties was also examined. Our method for constructing multilayer films containing protein cages is expected to be useful in building more complex functional inorganic nanostructures.     

Interrelations of discrete Painlevé equations through limiting procedures

We study the discrete Painlevé equations associated to the affine Weyl group which can be obtained by the implementation of a special limits of -associated equations. This study is motivated by the existence of two -associated discrete both having a double ternary dependence in their coefficients and which have not been related before. We show here that two equations correspond to two different limits of a -associated discrete Painlevé equation. Applying the same limiting procedures to other -associated equations we obtained several -related equations most of which have not been previously derived.     

Platinum supported on CeO2 effectively scavenges free radicals within the electrolyte of an operating fuel cell

CeO(2), Pt/CeO(2) and MnO(2) additives were found to lower the rate of free radical induced polymer electrolyte membrane degradation in an operating fuel cell by over one order of magnitude.     

Thermoelectric power of cerium up to 6 GPa

The thermoelectric power (TEP) of cerium has been measured up to 6 GPa. The results have been interpreted using the theories developed by Blandin et. al. and Hirst.     

Biodegradability of polylactide bottles in real and simulated composting conditions

As new biodegradable polymers and their packaging applications are emerging, there is a need to address their environmental performance. In particular, there is a need to understand the time required for their complete disintegration, before these materials are deployed in commercial composting processes. Standards developed by ASTM and ISO evaluate the biodegradation of biodegradable plastic materials in simulated controlled composting conditions. However, a more detailed understanding of the biodegradation of complete packages is needed in order to have a successful composting operation. This paper investigates the biodegradation performance of polylactide (PLA) bottles under simulated composting conditions according to ASTM and ISO standards, and these results are compared with a novel method of evaluating package biodegradation in real composting conditions. Two simulated composting methods were used in this study to assess biodegradability of PLA bottles: (a) a cumulative measurement respirometric (CMR) system and (b) a gravimetric measurement respirometric (GMR) system. Both CMR and GMR systems showed similar trends of biodegradation for PLA bottles and at the end of the 58th day the mineralization was 84.2±0.9% and 77.8±10.4%, respectively. PLA bottle biodegradation in real composting conditions was correlated to their breakdown and variation in molecular weight. Molecular weight of 4100 Da was obtained for PLA bottles in real composting conditions on the 30th day. The biodegradation observed for PLA bottles in both conditions explored in this study matches well with theoretical degradation and biodegradation mechanisms; however, biodegradation variability exists in both conditions and is discussed in this paper.     

Extracting the frequencies of the pinna spectral notches in measured head related impulse responses

The head related impulse response (HRIR) characterizes the auditory cues created by scattering of sound off a person's anatomy. The experimentally measured HRIR depends on several factors such as reflections from body parts (torso, shoulder, and knees), head diffraction, and reflection/ diffraction effects due to the pinna. Structural models (Algazi et al., 2002; Brown and Duda, 1998) seek to establish direct relationships between the features in the HRIR and the anatomy. While there is evidence that particular features in the HRIR can be explained by anthropometry, the creation of such models from experimental data is hampered by the fact that the extraction of the features in the HRIR is not automatic. One of the prominent features observed in the HRIR, and one that has been shown to be important for elevation perception, are the deep spectral notches attributed to the pinna. In this paper we propose a method to robustly extract the frequencies of the pinna spectral notches from the measured HRIR, distinguishing them from other confounding features. The method also extracts the resonances described by Shaw (1997). The techniques are applied to the publicly available CIPIC HRIR database (Algazi et al., 2001c). The extracted notch frequencies are related to the physical dimensions and shape of the pinna.